Wouldn't it be simpler to just do:

my %found;

for ( 1 .. $length ) {
    my $P = Algorithm::Permute->new( \@input_chars, $_ );
    
    while ( my @res = $P->next ) {
        my $word = join '', @res;
        $found{ $word } = calc_score( $word ) if exists $words{ $word 
+};
    }
}
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And get rid of the @partials array altogether?

Also, the calc_score and calc_bonus functions could be combined:

sub calc_score {
    my @chars = split //, shift;

    my $val = 0;
    $val += $worth{ $_ } for @chars;

    $val += 50 if @chars == 7;

    my $bonus = 0;

    for ( @dl ) {
        $bonus += $worth{ $chars[ $_ - 1 ] } if $chars[ $_ - 1 ];
    }

    for ( @tl ) {
        $bonus += 2 * $worth{ $chars[ $_ - 1 ] } if $chars[ $_ - 1 ];
    }

    $bonus += $val if $dw;
    $bonus += 2 * $val if $tw;

    return $val + $bonus;
}
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